Oil and natural gas are extracted from subterranean formations by drilling boreholes into hydrocarbon-bearing zones, building a well completion, and then recovering the product. Various sensors are utilized in order to enhance both the creation of the borehole and the productivity of the completed well. For example, wireline and logging-while-drilling sonic tools are utilized to measure the dynamic elastic properties of the formation around the borehole using compressional and shear velocity measurements. When the elastic properties of the formation are anisotropic, several velocities can be measured and used to partially or totally characterize the anisotropic elastic tensor, depending on the propagation and polarization direction. Various conditions can cause anisotropy, including but not limited to intrinsic rock properties, fractures, and non-equal principal stresses. The latter condition has some implications for wellbore stability, optimal hydraulic-fracturing, completion design, and other geophysical and petrophysical applications. Proper identification of the cause of the anisotropy is therefore important.
Certain techniques for identification of the cause of anisotropy are known. Monopole P- and S-waves, monopole Stoneley and cross-dipole shear sonic data in the anisotropic formation can be used to estimate one compressional and three shear moduli [Sinha, B., et al., Radial profiling of three formation shear moduli, 75th Ann. Internat. Mtg. Soc. of Expl. Geophys., 2005; U.S. Pat. No. 6,714,480, entitled “Determination of anisotropic moduli of earth formations”, to Sinha, B., et al., issued Mar. 30, 2004, incorporated by reference herein in their entireties.] An orthorhombic formation with a vertical symmetry axis is characterized by three shear moduli: c44, c55 and c66 In a vertical borehole, two vertical shear moduli (c44 and c55) can be directly estimated from azimuthal anisotropy analysis of cross-dipole waveforms. Fast-shear azimuth can be calculated using a method such as Alford rotation, and fast- and slow-shear slownesses can be estimated from the zero-frequency limits of cross-dipole dispersions [Alford, R. M., Shear data in the presence of azimuthal anisotropy, 56th Ann. Internat. Mtg., Soc. of Expl. Geophys. 1986; Esmersoy, C., et al., Dipole shear anisotropy logging, 64th Ann. Internat. Mtg, Soc. of Expl. Geophys., 1994; Sinha, B., et al., Radial profiling of three formation shear moduli, 75th Ann. Internat. Mtg. Soc. of Expl. Geophys., 2004; U.S. Pat. No. 5,214,613, entitled “Method and Apparatus for Determining Properties of Anisotropic Elastic Media” to Esmersoy, C., issued May 25, 1993; U.S. Pat. No. 5,808,963, entitled “Dipole Shear Anisotropy Logging”, to Esmersoy, C., issued Sep. 15, 1998, or for an alternative method see U.S. Pat. No. 6,718,266, entitled “Determination of dipole shear anisotropy of earth formations” to Sinha, B., et al., issued Apr. 6, 2004; Tang, X., et al, Simultaneous inversion of formation shear-wave anisotropy parameters from cross-dipole acoustic-array waveform data, Geophysics, 1999, incorporated by reference herein in their entireties]. The third shear modulus, c66, can be estimated from the Stoneley data, provided corrections are applied to remove any near-wellbore alteration and tool effects [Norris, A. N., et al., Weak elastic anisotropy and the tube wave, Geophysics, 1993, 58, 1091-1098; U.S. Pat. No. 6,714,480, entitled “Determination of anisotropic moduli of earth formations” to Sinha, B., et al., issued Mar. 30, 2004, incorporated by reference herein in their entireties]. Dipole dispersion curves are then used to identify the cause of the anisotropy of the elastic properties: (i) stress-induced effects (due to far field non equal principal stresses and near field stress concentration around the borehole) using the characteristic crossover of the dipole curves [Sinha, B. K., et al., Stress-induced azimuthal anisotropy in borehole flexural waves, Geophysics, 1996; Winkler, K. W., et al., Effects of borehole stress concentrations on dipole anisotropy measurements, Geophysics, 1998; Sinha, B. K., et al., Dipole dispersion crossover and sonic logs in a limestone reservoir, Geophysics, 2000; U.S. Pat. No. 5,398,215, entitled “Identification of Stress Induced Anisotropy in Formations” to Sinha, B., issued Mar. 14, 1995, incorporated by reference herein in their entireties], or (ii) intrinsic- or fracture-induced anisotropy using the characteristics of parallel dispersion curves [Sinha, B. K., et al., Borehole flexural modes in anisotropic formations, Geophysics, 1994; U.S. Pat. No. 5,398,215 entitled, “Identification of Stress Induced Anisotropy in Formations” to Sinha, B., issued Mar. 14, 1995, incorporated by reference herein in their entireties]. However when both fracture and stress effects are present, or when the analysis of dispersion curves is difficult to interpret due to attenuation of high frequencies [Donald, A. et al., Advancements in acoustic techniques for evaluating natural fractures, 47th Annu. Logging Symp., SPWLA, 2006, incorporated by reference herein in its entirety.], or when the symmetry axis of the anisotropic medium and the borehole axis are not aligned, the interpretation of the observed anisotropy becomes more challenging. Independent information has to be provided to confirm the observations and discriminate the relative importance of the different effects.
Discriminating the relative importance of the different effects is especially important when the principal stress directions and the normal to the natural fracture planes are not aligned. The analysis of the Stoneley mode reflections and attenuation allows the identification of open fractures in the borehole, and an estimation of their apertures [U.S. Pat. No. 4,870,627, entitled “Method and apparatus for detecting and evaluating borehole wall to Hsu, K., issued Sep. 26, 1989; Hornby, B. E., et al., Fracture evaluation using reflected Stoneley-wave arrivals, Geophysics; 1989; Tezuka, K., et al., Modeling of low-frequency Stoneley-wave propagation in an irregular borehole, Geophysics, 1997; U.S. Pat. No. 4,831,600, entitled, “Borehole Logging Method for Fracture Detection and Evaluation” to Hornby, B., issued May 16, 1989, incorporated by reference herein in their entireties.] In addition, the interpretation of borehole images (electrical and ultrasonic) can be used to identify either open or closed fractures [Luthi, S. M., Geological well logs: their use in reservoir modeling, Springer, 2000; U.S. Pat. No. 5,243,521, entitled, “Width determination of fractures intersecting a borehole” to Luthi, S., issued Sep. 7, 1993, incorporated by reference herein in their entireties.] Fracture properties such as location and orientation can then be calculated. However, no practical technique exists for forward quantitative modeling of both natural fracture- and stress-induced sonic anisotropy in order to discriminate their relative effects.